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First we need to change the limits, and by plugging in 1 and 0 to our substitution we find that the limits for u are arctan(1) and arctan(0) (or pi/4 and 0). Then we need to substitute for dx, and by diff...

M=37.5e^kt 52=37.5e^k5 52/37.5=e^5k ln(52/37.5)=5k (1/5)(ln(52/37.5))=k k≈0.06538 when t=9, M=37.5e^9*0.06538 M=67.54

This question is looking at integration by parts. Therefore, we need to split the integral into two parts.

Part A will be x³ and Part B will be e^x .

Draw 2 columns putt...

Firstly, let (x-2)/((x+1)(x-1)²) = A/(x+1) + B/(x-1)+C/(x-1)², where A,B and C are to be calculated. 

Then, multiply both sides of the equation by (x+1)(x-1)^2<...

Every term needs to be differentiated in terms of x:

For the x³ term, differentiated it becomes 3x² (multiply the whole term by the initial p...